Given any set , there is a unique empty family of elements of . Formally, this is given by the empty function to , the unique function from to from the empty set. As the empty set is finite and (a fortiori) countable, this empty family counts as a list and a sequence; in such a guise it is known as the empty list or the empty sequence.
When treating it as an element of the free monoid on , the empty list may be written , , or , perhaps with a subscript if desired.
Similarly, we have the notions of the empty family of elements of a preset or other notion of type, the empty family of objects and the empty family of morphisms of a given category, and more generally the empty family of whatever you want.